Question

z varies directly as √x and inversely as y². If z = 241 when x = 36 and y = 4, find z if x = 81 and y = 6. (Round off your answer to the nearest hundredth.)

Answer 1

To find z given z varies directly as the square root of x and inversely as y squared, we can use the direct and inverse variation equations. Substituting the given values, we can solve for the constant of variation k, and then substitute the new values of x and y to find z.

Step-by-step explanation:

To solve this problem, we can write the direct variation equation as z = k√x, where k is the constant of variation. We can also write the inverse variation equation as z = k/y². Substituting the given values, we can find the value of k and then substitute the new values of x and y to find z.

First, for the given values of z = 241, x = 36, and y = 4, we can write the equation as:

241 = k√36/y²

Simplifying, we get:

241 = 6k/4

241 * 4 = 6k

964 = 6k

k = 964/6

k = 160.67

Now, we can substitute the new values of x = 81 and y = 6 into the direct variation equation:

z = 160.67√81

Using a calculator, we find that:

z ≈ 429.10 (rounded off to the nearest hundredth)

Learn more about Direct and inverse variation